Sometimes people say that water is removedu zis;8o/h8mao ui;v; from clothes in a spin dryer by centrifugal force throwing the water outward. What is wrong with this stateoo ;hi v;uiz sa88/;umment?

Will the acceleration of a car be the same when the car traved6,(fdk/yu3e b /xhr nls around a sharp curve at a constant 60 km/ny xf /ed3, k(uh6rdb/h as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Where does the cae+ci h+/rr5rk; )pbetr exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretch near thr / ;phk5e crrib+et+)e bottom of a hill?

Describe all the forces acting on a child rid( ok qpwd+6/1h3.xf3qboxsrp ing a horse on a merry-go-round. Which of these forces provides the centx/ r1kf+qpob6x3shq d.w (p3oripetal acceleration of the child?

A bucket of water can be whirled in a vertical circle without thqy-cv or;dwj--4 nzw5e water spilling out, even at the top of the circle when the bucket is upside down. Explainy-d- wocnq ;-v4zw 5rj.

How many “accelerators” do you have in j:ys5pctnjz,m-;ng av 6r.8hyour car? There are at least three controls in -6trsazy,p mhnj5nv. 8;:cgj the car which can be used to cause the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the cr3 hd z0zv(lbp8t+-hbp est of a small hill, as shown in Fig. 5–31. His sled does not leave the (vbl -d0 hp 3+tzzpb8hground (he does not achieve “air”), but he feels the normal force between his chest and the sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when rounding a curve rn+x tsu g402vat high speed?

Why do airplanes bank when they turn? How would you compiv . 066*nl j+w iluvkfw9h0m-p cflt+ute the banking angle give k.fvliunplw+jf6 -69+lh 00im*v cwtn its speed and radius of the turn?

A girl is whirling a ball on a string around her head ,* p 2xch;28rgisksb6s xnmuz 6w*pvx* dz(9uin a horizontal plane. She wants to let go at precisely the right time so that the ball will hit a target on the other side of the yard. When shov2i6s mhzn8b ;uu ,gsdw9p6*2csx kp(* x*xrzuld she let go of the string?

Does an apple exert a gravitational force on,z8z1g: p l-jalr* nwz the Earth? If so, how large a force? l1gzjnwp,*z8:l- zraConsider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what )s;dsmoif1hjo r0lt -2)5xpsways would the Moon’s orbit be di)jss sd ho 1 xmotfl2i-0r5)p;fferent?

Which pulls harder gravitationa4a c.o,ze p:2eyve) .c +a5biajjrdt.lly, the Earth on the Moon, or the Moon on the Earth? Whic4.ce+5ed ., bza: )yjp.aj cr2teao vih accelerates more?

The Sun's gravitational pull on tv,3yyqfrj*l f e h 97+cduj7i7he Earth is much larger than the Moon's. Yet the Moyu7crd7jhfq*vj3e +if, 79l yon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equator or at the poles? Whatmbg7xd14- :x*ha vuvv two effects are at work?dhx vu 1b:7 ax*vg4-mv Do they oppose each other?

The gravitational force on the Moon due to the Earth is only gr 352z +dbhsymni*b m/a;j8mabout half the force on the M;bb *m+a h2s5m8zg3n/yij rm doon due to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars icvft (gmu2 8/dsk, (rj0pdpjd8oa :v1n its orbit around the Sun larger or smaller t/d88(: j opu sa,vc10(m d2 tdvkrfjgphan the centripetal acceleration of the Earth?

Would it require less speed to launch a satellite (a) toward the east or (b) 65en qxw ei4/e)o 7t 3)itqrlbtoward the west? Consider the Earth’ iilxo4tt/r6e5 ne 3))ewq 7bqs rotation direction.

When will your apparent weight be the greatest, as measured by a efz u)m 1icbe usqii1/65 (2 nfnm)pv5scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? When would it be the(z nq vb15 i) ec/mimfnfs56uup 2e)1i same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer space could be adversely af1 f-ef;zxo, brfected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall,z-fo ;e ,1rfbx (b) the force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner expeu3(ip(; llbmvriences “free fall” or “apparent weightlessness” between stepu(lpv(3 l bmi;s.

The Earth moves faster i k.juv f9l:e9mn its orbit around the Sun in January than in July. Is the Earth closer to the Sun in January,e.kv9 mu:9lfj or in July? Explain. [Note: This is not much of a factor in producing the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until it was discovered to hm u2q28kpz.4f vfy .spm7ao v)ave a moon. Explain how 82p2)m ofqf.up4zv.mksyv7athis discovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much+;lj nbo km9:mkvr5/k larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A child sitting 1.10 m from the center of a merry-go-round moves with a speed of 5/k;jk:+9ovkrblm nm 1.25 $\mathrm{~m} / \mathrm{s}$ . Calculate (a) the centripetal acceleration of the child,   
(b) the net horizontal force exerted on the child ( mass =25.0 $\mathrm{~kg}$)   

  A jet plane traveling 1980o. )vne6 xsxv5 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ pulls out of a dive by moving in an arc of radius 6.00 km . What is the plane's acceleration in $g^{\prime}$ 's?    g's

  Calculate the centripetal acceleration of the Earth in its orbit g4clki o/wq6 .around the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's orbit is a circle of radius 1.6.wk 4ocg qi/l50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exerted on a 2.0-kg discus as it rota1 ek;lotdv6(x tes uniformly in a horizontal c;(vokld6xe1 t ircle (at arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the E;, km:j1h/ayfmtwp:;lrt/ vcy;tf) p arth's surface, and circles the Earth about once every 90 minut htl;v/rmf; maf;yt :t/p p,y )wc1:kjes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck o,dw+uo la b05 v3unxr h7sj0*xtj:tt/ f clay on the edge of a potter’s wheel turning at 45 rpjsa7hlx/b3 tv r,dj5*t:0 tou uw+x0nm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate iq hq3n sehuav :uj4c74hpq,04 p:x6yon a vertical circle of radius 72.0 cm , as sy :n4uhqh0j u4,qcqvspea4h76pox3 : hown in Fig. 5-33. If its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

  A 0.45$-\mathrm{kg}$ ball, attached to the end of a horizontal cord, is rotated in a circle of radius 1.3 m on a frictionless horizontal surface. If the cord will break when the tension in it exceeds 75 N , what is the maximum speed the ball can have?   

  What is the maximum speed with which a 1050-kg car can round a turn of7 , eeqv*f*47mngsef t radius 77 m on a flat road if the coefficient of static friction between tires and road is 0.80? Is thf 7mv*eetq7 sfn,eg4*is result independent of the mass of the car?   

  How large must the coefficient of static friction be between the tires and th0.aqc )scs2q qe road if a car is to round aa20 c.scqsq )q level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is designedrb76p4msk2en atdl; 6 to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on her back is 7.85 times her own weight, how fast is she rotadkm24lnb6e ta7 ;pr6sting?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the axmjmy6bq gr 9v,pvh9.9 ce(yb)is of a rotating turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 r m9cvbb.y,em6pr)j9yh q g(9 vpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be traveling when upside dy yg8u, 8*x:*hwnwzg wown at the top of a ci8gxgww*wh,8*:y yz nurcle
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of mass 950 kg (including the driver) crosses 2 uxn1 eu9fnrt5-,vd zthe rounded top of a hille59frxn,nt v-u d2z1u (radius =95$ \mathrm{~m}$ ) at 22 $\mathrm{~m} / \mathrm{s}$ . Determine
(a) the normal force exerted by the road on the car,   
(b) the normal force exerted by the car on the 72-kg driver   
(c) the car speed at which the normal force on the driver equals zero.   

  How many revolutions per minute would a 15-m-diametev;) p zwdvw(e4r Ferris wheel need to make fov(; v4z)dp wwer the passengers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vdt3mjc1d o m*3(8i- uwi5trbeertical circle of radius 1.10 m. At the lowest point of its motion the -o3dc3ime wjmiu8t*td5( 1rb tension in the rope supporting the bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a centrifuge rotate if a particle 9.00 cm from th59f ubc+j ,o.ju2mcd oe axis of rotation is to experience an acc. djucoum9bf+ j5,c2oeleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, pjcvr2m 2xbb 8 5vm1hk/k4v(eieople are rotated in a cylindrically walled "room." (See Fig. 2h5128kxm mbvjirvk(4ev cb/5-35.)
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is rotatap/ a6qokjeep 9.dn +:ed in a circle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) through a central hole as shown in a./6e qn9d eo+ jpap:kFig. 5-
36. Show that the speed of the puck is given by

$v=\sqrt{\frac{m g R}{M}}$

  Redo Example 5-3 , precisely this time, by not ignoring the weigh / u-tf+jv4zuq*vaad0t of the ball which revolves on a string 0.600 m long. In partit-j f a/ zuvdv+0q4*uacular, find the magnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius ofn.tblb5b ybj-i o/.3 f 88 m is perfectly banked for a car traveling 75 $\mathrm{~km} / \mathrm{h}$ , what must be the coefficient of static friction for a car not to skid when traveling at 95 $\mathrm{~km} / \mathrm{h}$ ?   

  A 1200$-\mathrm{kg}$ car rounds a curve of radius 67 m banked at an angle of 12$^{\circ}$ . If the car is traveling at 95$ \mathrm{~km} / \mathrm{h}$ , will a friction force be required? If so, how much and in what direction? $\approx$    down the plane

Two blocks, of massefs ae2*ji wp57s $ m_{1}$ and $m_{2}$ , are connected to each other and to a central post by cords as shown in Fig. 5-37. They rotate about the post at a frequency f (revolutions per second) on a frictionless horizontal surface at distances $r_{1}$ and $r_{2}$ from the post. Derive an algebraic expression for the tension in each segment of the cord.

  A pilot performs an evasive maneuver by diving vertica4 )gowgsm8u+ zlly at 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential and centr.w*pp+ng pv) suwx/ /mipetal components of the net force exerted on the car (by the ground) in Example/u * pmpnwvx g/)w.ps+ 5-8 when its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolisv (o6b+ 8scn4k cw+dsdk 1xz.w 500 accelerates uniformly from the pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when v(z d6b+.cw8 sc4xk+nkds1 woit is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal a69/p u9p/ffn+aca gpcircle of radius 2.90 m . At a particular instant, i 99fa paucpf/ap g+n6/ts acceleration is 1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Earth’s gravixsqs( rkhs*m1 c+- 5zmhc;vjmd6b() h ty on a spacecraft 12,800 km (2 Earth radii) d*hz -c6mhsqm m ;(v +1sxhrjs()k 5cbabove the Earth’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational accel)pp,t k0ax fmje2uswi /(2*cferation g has a magnitude of 12 m/2xp)f e0aw2*u, (mtsp icjkf/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gr5vxbf2 asar dq4 ox3u+/8u2rv avity on the Moon. The Moon's radius is 1.7f/s b8v+22uo 3uxrr xq4ad5a v4 $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a r xg(f 5iu7phpj 7)vkpq* td)l8adius 1.5 times that of Earth, but has the same mass. What is the acceleration due to gravity nead() lf5p7*g7ppi jkhu)8tqvx r its surface?   

  A hypothetical planet has a mass 1.66 ticqxth62x ;eg6won:i6fy b ;6xhe1h isd ;b7t (mes that of Earth, but the same radius. What is g near i6hwee yg12; t;6b7;so6:d6ftnhcq bxi (ixhxts surface?   

  Two objects attract tam dz0v 8)65g nhjrg3)aqvamtp/:7eeach other gravitationally with a force of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value 6mc tl8 axcoe i1ahx-0 5* vjf7p/zrt+emo/,gof g , the acceleration of gravity, at (a) 3200 mtco06+vfoa e, /e5/mr1mx zl8i cxj*-p7at gh    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the E3o exuuf-p:0gahy.jt-tq7,bt c2,wy 7 xl 1ydarth where thegravitational acce7uqw,b x th -0a2eyot71:.xu,y3cylft gd p-jleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star hc.,vq4uh0dc4 jwtvr/as five times the mass of our Sun packed into a sphere about 10 km in radius. Estimatec .0du/4vqwjc 4r tv,h the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which oncej6o v3u /phuu,xk-yg4 was an average star like our Sun but is now in the last stage of its evolution, is the size of our Moon but has the mass of our Sun. What is the sur,vg3/juup h64 -kouxyface gravity on this star?    $\times 10^7$

  You are explaining why astronauts fee.m,chtgnc g ) tx/f1l:2 nn: cs .l7rk,wlp4scl weightless while orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculam :)n/ 17ck4xl . ch,n sg.wgt,cnfrl :lts2cpting the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are *hzx7ub+-4kc sugw2vdzn;zp k7 *5 xflocated at the corners of a square of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted on n*4wpc5ub z z*k277+ husxvdkg f;-zxone sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years/7z f2gs2lg5zc;gy0or epl 7h most of the planets line up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming aeg;/lrz fy7phs oz2l205ggc7 ll four planets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of gpm qf )c,a3 0e4h3i4 mbojy*l 0c7lmxmravity at the surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, dmbemm, * o03cx qf)l majlcy74hi0p43etermine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Su3r t juaetr,l hm3.y2-n using the known value for the period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtair-a3,u3mejtt .2 lr hyned using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed hq1nph), qal 9f0oy5eof a satellite moving in a stable circular orbit about the Earth at a height of 360 e5a yplqofh,qn 9h01)0 km.    $\times 10^3$

  The space shuttle releases a satellite i: ;kndtd 2uye*cm 6-z5.vibymnto a circular orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) when the c. me vty;-2u5:ydzm n6k*bdirelease occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occup2vo:ak5, iajgants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and giveia2j5vao,g k: your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the Earth in a circuu.pw -34ldwhz wzpq6e; 4zm 3ylar “near-Earth” orbit. A “near-Earth” orbit is one at a hum34zdz y3l-; wpq4ewhwp .6zeight above the surface of the Earth which is very small compared to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be launched froma: tdg+,jx:wt the top of Mt. Everest to be plj :d+ax: ,gwttaced in a circular orbit around the Earth?   

  During an Apollo lunuztbe e okr. guxt2*g8l2+8 t0ibi:z8ar landing mission, the command module continued to orbit the Moon at an altitude of about 100 km. How long did it taket2 u8i.8ugb x 2gok8*e +zb0rtte:liz to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit the planer+y4 x36ejlwgs;)yd q t. The inner radius of the rings is 734re+lx syyq;jw g)63d,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


$T_{\text {irner }} $ =   
$T_{\text {outer }} $ =   

  A Ferris wheel 24.0 m in diameter rotates once every 15.5 s (see/laa8t yb l)4g Fig. 5–9). What is the ratio of a person’s apparent weight to her real weight (a) at bl )al4ty a/g8the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 kj1 kxy*s5,i /h,b16i-lu infqe mcb7sm from the center of the Earth's Moon in ej15sm7uk6nx yiq1li,bb *cs fhi,-/ a space vehicle (a) moving at constant velocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star system consists of two stars of equal mojlk(hef 250hass. They are observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway between them. What is tf0jehl 5okh (2he mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a1rp0bq6nzdw ru)g 0 wjotr;f(c6y, m2 55-kg woman in an elevator that movb1frjrqz 0(wm;o p26t0g d)u cnryw6,es
(a) upward with constant speed of 6.0m./s   
(b) downward with constant speed of 6.0m./s   
(c) upward with acceleration of 0.33 g,   
(d) downward with acceleration 0.33 g   
(e) in free fall?   

  A 17.0-kg monkey hangs from a cord suspended from the ceiling of an i48r jaa+n )c flhan 1)4bmlb0elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the eh41 08 4bc)aaan+ b)mjnl ilfrlevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orb0v( h ):y4ed j1funeobits very near the surface of a planet with period T , the density (mass/volume) ofy0vou1 )4jdhb(en e:f the planet is $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the period of the Moon (27.4 d) to determinez 9q:+ch in-a/ny;qhn the period of an artificial satellite orbiting very near the Earth-z ych+;h/ n9a :niqnq’s surface.    s

  The asteroid Icarus, though only a few hundred meters across,q/yr4c8i7uz r hz ugq2,h)go/ orbits the Sun like the planets. Its period is 410 d. What is itr,)hgquh/u/ zozi7qr 4 g8cy2s mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance ofctv7vfp; 3gnfqq :;is. v-ib 3 4.5 $\times 10^{9} \mathrm{~km}$ from the Sun. Estimate the length of the Neptunian
year given that the Earth is 1.50 $\times 10^{8} \mathrm{~km}$ from the Sun on the average.    $\times 10^2$

  Halley’s comet orbits the Sun roughly once every 76 years. It com e3kt-bo-1b bpwzx 3vsl3.po( es very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from th(wbe333kotb-. sb- vpx o1l pze Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the cenumac,egaj +*ay .41odter of the Galaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, period, and mean distance for the four29f dahfkw19 r-rfwm6 largest moons of Jupiter (those discovered by Galileo rr9d6 9 1fhf2-fwkaw min 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Earth from theewe5j37 l-o d:wso;lb known period and distance of the Moon. ls ojw ee;- b35wod7:l   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moons, usingksp)c jde/* vr(.ulbar069w r Kepler’s third law. Use the distance ofu 9s6 pk0cav)jrr. wl( /d*reb Io and the periods given in Table 5–3. Compare to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter consists ofj:hy wlq fee/p6+/f c6bz77ok many fragments (which some space sc7yefec67kp/ :l +wjf/boh zq6ientists think came from a planet that once orbited the Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artiq,);s.dj,qarv*a*d 2h5ia y vk z,yi)tml +tificial "planet" in the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revoluhd 5yi+ j liv qizs )y a,,)qaa**,vttm.;rkd2tion, this planet's year, in Earth days?   

  Tarzan plans to cross a(0 qeagatf4*p gorge by swinging in an arc from a hanging vine (Fig. 5–41). If his(0ae4gq fap*t arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration of gravity bxg:(h 1*lga6fvgrk/r go mg jb 478q+ce half what fgm :gvh/bgk6g*g4a(xrr17c+ljo 8 qit is on the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass gr y;j0hn*wld0k 1xny9 yab hands and spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their indiv hy0dlj;nx0kyyn* 1w9 idual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acceleration o -x-*gcg l;8;e0e ywpm6eitxxq v;5fof gravity at the equator is slightly less than it would be if the Earth yemt-ole ; x 8x0f*xi-;6qcp gevg5;wdidn’t rotate. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft travbb -*jw izhpv;zc843* m jb+bcl )+olgeling directly from the Earth to the Molgb-p * zwjiv8lzh3j b c)+bcbm;4*o+ on experience zero net force because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kqww *o2prdw +6k de0)yg, but when you stand on a bathroom scale in an elevator, it says your mass is 82 k6w2)w p*dywko e0 +drqg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station jezas4*x *p*tconsists of a circular tube that will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per day) *pt4 * xe*jazsif an effect equal to gravity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical5w3uqed;mx/ ;p 8va nj ny(l6p loop (Fig. 5–43).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the mass of a planety3c(mr- f/9ij jd ;ut+dxx 0rg in terms of its radius r, the acceleration due to gravity at its9frrc3-utg0 d+xj(miyd/ jx ; surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected from the verticain/ n(;x84z 5ee kwy uk4wv,uhl by an x(4wnke;wuyue8, n i4 /v zhk5angle $\theta$ due to a massive mountain nearby (Fig. 5-44). (a) Find an approximate formula for $\theta$ in terms of the mass of the mountain, $m_{\mathrm{M}}$ , the distance to its center, $D_{\mathrm{M}}$ , and the radius and mass of the Earth. (b) Make a rough estimate of the mass of Mt. Everest, assuming it has the shape of a cone 4000 m high and base of diameter 4000 m . Assume its mass per unit volume is 3000 kg per $ \mathrm{m}^{3}$ . (c) Estimate the angle $\theta$ of the plumb bob if it is 5 km from the center of Mt . Everest.

A curve of radius 67 m is banked for a design speed of ma:mv pe9*6sbf)q j 8rre* +yu If the coefficient of static friction is 0.30 (wetu*mrjey:v+*mqrsea 6) 8 bfp 9 pavement), at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth werqduywe8c 03 ur7t bd9+e rotating so fast that objects at the equator were appa d73ude 9r08tqb+yc wurently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance amlsmf c7) 5.fgpart of 8.0 $\times 10^{10} \mathrm{~m} $ and rotate about a point midway between them at a rate of one revolution every 12.6 yr . (a) Why don't the two stars crash into one another due to the gravitational force between them?
(b) What must be the mass of each star?    $\times 10^{26}$

  A train traveling at a c6q 13 bubruti46/tymkonstant speed rounds a curve of radius 235 m. A lamp suspended from the ceiling swings out to an t6ymbqu 6u /k3i4t rb1angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as th( (7nr94n mtbpv- bgem4c nyi*e Earth. Thus, it has been claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate r9ti4c (m b *egnb(pm4- nyn7vthe number of g 's a person would experience at the equator of such a planet. Use the following data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Space Telescope deduced the presence or4/usio9/5 8cfz pqupf an extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light escapeuq8czfiporsu/ /9 p54 s). They did this by measuring the speed of gas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as it traverses the hill and valley shown v,vy wdj xof;88.+pgzy5zf 6q in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where wzodz6 fx y.y+fg ;5,wjvv8q8p ould the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilizes a group of 24 satelpamf* 4 ig:5dmndy -mss)(qe1lites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approxi1dym( sqp*) s4af gmmni:de5 -mately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), after traveling 2.1 billion km, is m*45d w1m;y 8m wyje97 ctfzhdceant to ortf8dej ;z74dy9hw cm1yc*5m wbit the asteroid Eros at a height of about 15 km . Eros is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in then+ ;5okngbqv)9fa 7ar space shuttle pursuing a satellite in need of repair. You are in a circular orbit of the same radius as the satellite (bon vr5ag+;)7q a9k nf400 km above the Earth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a period of 3000 years. (a) What is its;kby9 ac2wjrk:;nn,r 2le9 pw mean distance from the Spae2 9r29nclrk,:by;;k w jwnun?   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the valu08.x r5act/pmf) cwmx dy0ig-e of G would need to be if you could actually "feel" yourself gravitationally attracted to someone near you. Makcrtmf0a.)x g c5/ -xmidp80wye reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around thes( 6uoag-8p nj center of the Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-years fr ap8- (s6gojunom the center $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at th fln9/-dxej u-e corners of a square 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottom side un- jeflx-/d9of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits the gd7x3jm(zy i.Earth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration exkks ,4s*fc s9yperienced by the tip of the 1.5-cm-long sweep second hand on your w,k 94skc*ssy frist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker y;zccz xk2p)q(-zfn3./ x gkzlsa,3aweight around in a circle below you on a 0.25-m piece of fishing line. The weight makes a complete circle every 0.50 s. What is the angle that the fishing lisclc)z.f yxkzgnq;,(2/p 3x- k aa zz3ne makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designed so that a car tr6 x-bjz8l oqo:aveling at spe:oz o-jbl68 xqed $ v_{0}$ can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from $v_{\min }$ to $v_{\max }$ . Derive formulas for $ v_{\min }$ and $ v_{\max } $ as functions of $\mu_{s}, v_{0}$ , and R .

  Amtrak’s high speed train, the Acela, utiliz),pl ufld bb2)+v6 bewes tilt of the cars when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling mopu2wbdfb + 6e)vl )l,bre comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ). (a) Calculate the friction force needed on a train passenger of mass 75 kg if the track is not banked and the train does not tilt. $\approx$    $\times 10^2$
(b) Calculate the friction force on the passenger if the train tilts to its maximum tilt of 8.0º toward the center of the curve.$\approx$    $\times 10^2$